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# Econ 409 B. Brown Spring 2013 EXERCISE 5 Consider the following aggregate data in 1958 dollars (millions):

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Econ 409 B. Brown Spring 2013 EXERCISE 5 Consider the following aggregate data in 1958 dollars (millions): Year Consumption Disposable Assets Income ( C )( D )( A ) 1946 127,235 147,089 728,310 1947 135,695 149,006 802,460 1948 145,757 165,261 889,960 1949 147,297 164,484 940,990 1950 154,992 180,434 953,090 1951 170,801 196,402 1,063,560 1952 181,179 205,950 1,151,240 1953 191,393 218,940 1,196,940 1954 197,958 223,308 1,225,210 1955 209,268 238,679 1,318,290 1956 222,854 253,903 1,427,030 1957 236,464 266,794 1,514,460 1958 246,247 273,516 1,555,700 1. Duesenberry considered the following model for aggregate consumption: C t = α + βD t + u t where u t is an unknown disturbance term. a. Run an OLS regression based on this specification and report ˆ α and ˆ β. b. Making explicit the assumptions you are making, what are the properties of your estimates ˆ α and ˆ β. c. Test the null hypothesis that the marginal propensity to consume is one. d. Discuss the properties of your test under the alternative that β is less than one. 2. Analternativemodelisbaseduponsavingbehaviorandcanbewritten: S t = α + βD t + u where S t = D t C t . a. Obtain OLS estimates of α and β. b. What is the relationship between the slope coefficient here and in the preceding problem? c. Rank (if possible) this regression and the previous regression. d. Test the hypothesis that β in this model is one. e. Calculate a 95% confidence interval for ˆ β . What is the relationship of this interval to the hypothesis test above. 1
3. Ando and Modigliani considered the model: C t = α + βD t + γA t + u Run this regression and report α , β ,and γ. a. Test whether γ , the coefficient for the “wealth” effect, is different from zero. b. Calculate the prob-value for b γ under the null of γ =0 . What is the relationship of this value to the hypothesis test. c. Test the joint hypothesis that β =1 and γ =0 . d. Compare and rank (if possible) this regression with the regression from (1). 2

The way to approach this... View the full answer

1. Duesenberry considered the following model for aggregate consumption:
Ct = α + βDt + ut
where ut is an unknown disturbance term.
a. Run an OLS regression based on this specification and report...

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